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Thurston's Work on Surfaces (MN-48)

This book provides a detailed exposition of William Thurston's work on surface homeomorphisms, available here for the first time in English. Based on material of Thurston presented at a seminar in Orsay from 1976 to 1977, it covers topics such as the space of measured foliations on a surface, t...

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Bibliographic Details
Main Author: Fathi, Albert
Other Authors: Laudenbach, François, Poénaru, Valentin
Format: eBook
Language:English
Published: Princeton, New Jersey ; Oxford Princeton University Press 2022, ©2012
Series:Mathematical Notes
Subjects:
Dynamics
Homeomorphisms
Surface
Online Access:
Collection: DeGruyter MPG Collection - Collection details see MPG.ReNa
Table of Contents:
  • 1. An Overview of Thurston's Theorems on Surfaces
  • 1.1 Introduction
  • 1.2 The Space of Simple Closed Curves
  • 1.3 Measured Foliations
  • 1.4 Teichm¨uller Space
  • 1.5 Pseudo-Anosov Diffeomorphisms
  • 1.6 The Case of the Torus
  • 2. Some Reminders about the Theory of Surface Diffeomorphisms
  • 2.1 The Space of Homotopy Equivalences of a Surface
  • 2.2 The Braid Groups
  • 2.3 Diffeomorphisms of the Pair of Pants
  • 3. Review of Hyperbolic Geometry in Dimension 2
  • 3.1 A Little Hyperbolic Geometry
  • 3.2 The Teichm¨uller Space of the Pair of Pants
  • 3.3 Generalities on the Geometric Intersection of Simple Closed Curves
  • 3.4 Systems of Simple Closed Curves and Hyperbolic Isometries
  • 4. The Space of Simple Closed Curves in a Surface
  • 4.1 The Weak Topology on the Space of Simple Closed Curves
  • 4.2 The Space of Multicurves
  • 4.3 An Explicit Parametrization of the Space of Multicurves
  • A. Pair of Pants Decompositions of a Surface
  • 5. Measured Foliations
  • 5.1 Measured Foliations and the Euler-Poincar´e Formula
  • 5.2 Poincar´e Recurrence and the Stability Lemma
  • 5.3 Measured Foliations and Simple Closed Curves
  • 5.4 Curves as Measured Foliations
  • B. Spines of Surfaces
  • 6 The Classification of Measured Foliations
  • 6.1 Foliations of the Annulus
  • 6.2 Foliations of the Pair of Pants
  • 6.3 The Pants Seam
  • 6.4 The Normal Form of a Foliation
  • 6.5 Classification of Measured Foliations
  • 6.6 Enlarged Curves as Functionals
  • 6.7 Minimality of the Action of the Mapping Class Group on PMF
  • 6.8 Complementary Measured Foliations
  • C. Explicit Formulas for Measured Foliations
  • 7. Teichmüller Space

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